Higher-order assembly of microtubules by counterions: From hexagonal bundles to living necklaces

Abstract

Cellular factors tightly regulate the architecture of bundles of filamentous cytoskeletal proteins, giving rise to assemblies with distinct morphologies and physical properties, and a similar control of the supramolecular organization of nanotubes and nanorods in synthetic materials is highly desirable. However, it is unknown what principles determine how macromolecular interactions lead to assemblies with defined morphologies. In particular, electrostatic interactions between highly charged polyelectrolytes, which are ubiquitous in biological and synthetic self-assembled structures, are poorly understood. We have used a model system consisting of microtubules (MTs) and multivalent cations to examine how microscopic interactions can give rise to distinct bundle phases in biological polyelectrolytes. The structure of these supramolecular assemblies was elucidated on length scales from subnanometer to micrometer with synchrotron x-ray diffraction, transmission electron microscopy, and differential interference contrast microscopy. Tightly packed hexagonal bundles with controllable diameters were observed for large trivalent, tetravalent, and pentavalent counterions. Unexpectedly, in the presence of small divalent cations, we have discovered a living necklace bundle phase, comprised of 2D dynamic assemblies of MTs with linear, branched, and loop topologies. This new bundle phase is an experimental example of nematic membranes. The morphologically distinct MT assemblies give insight into general features of bundle formation and may be used as templates for miniaturized materials with applications in nanotechnology and biotechnology.cation ͉ like-charge attraction ͉ x-ray I n this article, we present our findings on the assembly behavior of microtubules (MTs), a model nanoscale tubule. MTs are hollow, cylindrical protein polymers, with inner and outer diameters of Ϸ15 and 25 nm, respectively, involved in a variety of cellular functions, including cell division, intracellular transport, and cell morphology. MTs often assemble into arrays and bundles as in axostyles in protozoa, the cortical array in plants, the mitotic spindle, and neuronal processes (1). MT-associated proteins (MAPs) regulate the interactions between MTs, giving rise to MT bundles with various degrees of order and different MT-MT spacings, both in native biological structures such as axons and dentrites and in in vivo overexpression experiments (2). In vitro experiments show that subtle mutations in MAPs can lead to bundles with radically different structures, converting hexagonally packed bundles into linear chains of MTs (3). However, it is unclear how MAP-controlled, MT-MT interactions lead to bundles with the observed architectures.Understanding the fundamental mechanisms underlying the nature of the self-assembly of nanometer-scale tubules and rods is also important from a technological perspective. Nanotubes are currently being developed as miniaturized materials with applications as circuitry components, templates for nanosized wires and optic...

Direct force measurements reveal that protein Tau confers short-range attractions and isoform-dependent steric stabilization to microtubules

“…2 D, bottom profile and E, bottom profile). As shown previously (5,67), the MT wall to wall spacing [D w-w = a H − 2 × (<R in > + w)] in the H MT phase can be quantitatively determined by measuring the X-ray structure factor (giving the hexagonal lattice parameter a H ) and simultaneously, the MT form factor, yielding <R in > and w. The structure factor was taken to be the sum of Bragg diffraction peaks at the reciprocal lattice vectors jG hk j = G 10 (h 2 + k 2 + hk) 1/2 and G 10 = 4π/(3 1/2 a H ). Each peak was represented as a squared Lorentzian: [A hk /(W q 2 + (q ⊥ − G hk ) 2 )] 2 , with G hk , amplitude A hk , and a single peak width proportional to W q (where 1/W q is approximately the bundle size in cross-section) as fitting parameters.…”

Equilibrium bundle size of rodlike polyelectrolytes with counterion-induced attractive interactions

“…However, the presence of multivalent counterions can actually induce an attraction between like-charged polyelectrolytes (PEs). This has been experimentally observed for several different PEs, including doublestranded DNA [2,3], F-actin [4,5], microtubules [4,6], and the fd, M13, and tobacco mosaic viruses [4,7]. Computer simulations of both homogeneously charged rods [8,9,10,11] and realistic DNA molecules [11,12,13] unambiguously show that attractive interactions can arise solely from counterion correlations not included in PB theory.…”

“…The correlation-induced attractive interactions lead to the formation of a "bond" of energy E bond = −γk B T L between each pair of neighboring rods in the bundle. If we assume that the rods in the bundle are packed in a hexagonal array, as has been experimentally observed [2,3,5,6], then, to a very good approximation for all M ≥ 2,…”

“…It is still a matter of discussion, however, as to which of these theories is the most appropriate description of the correlation-induced attraction seen in experiments and simulations. Furthermore, it is unknown whether the interactions between multiple rods is pairwise additive or not [17,20,21].Under experimental conditions in which the interaction between PEs is attractive, the PEs typically form dense, ordered bundles of a well-defined size, rather than precipitating into a PE-rich phase [2,3,4,5,6,7]. In this paper, we theoretically investigate the thermodynamic stability of these bundles (if bundle growth is not limited thermodynamically, then it must be limited by kinetic barriers [21,22,23]).…”

“…Under experimental conditions in which the interaction between PEs is attractive, the PEs typically form dense, ordered bundles of a well-defined size, rather than precipitating into a PE-rich phase [2,3,4,5,6,7]. In this paper, we theoretically investigate the thermodynamic stability of these bundles (if bundle growth is not limited thermodynamically, then it must be limited by kinetic barriers [21,22,23]).…”